The degree and radian measure of the angle between the hour-hand and the minute-hand of a clock at tweny minutes past seven is

  • Option 1)

    \frac{5\pi }{4}

  • Option 2)

    \frac{5\pi }{8}

  • Option 3)

    \frac{5\pi }{7}

  • Option 4)

    \frac{5\pi^c }{9}

 

Answers (2)

 

Sexagesimal System -

In this system, an angle is measured in degrees, minutes and seconds.

- wherein

1\ right angle = 90^{\circ}

1^{\circ} = 60{}'

1{}' = 60{}''

 

 Angle made by hour hand and minute hand is approx 100^{^{\circ}} degrees for past seven and two minute total length will be approx 16.6{ because there are 60 gaps and each gap having  \frac{360}{60}=6 measurement

\therefore total angle 16.6 X 6 = 99.6 \simeq 100{}'

\frac{5\pi ^{c} }{g}

[\because the hour hand rotates through an angle of 30^{\circ} in one hour or \left ( \frac{1}{2} \right )^{\circ} in one minute.]

 


Option 1)

\frac{5\pi }{4}

This option is incorrect.

Option 2)

\frac{5\pi }{8}

This option is incorrect.

Option 3)

\frac{5\pi }{7}

This option is incorrect.

Option 4)

\frac{5\pi^c }{9}

This option is correct.

Sexagesimal System -

In this system, an angle is measured in degrees, minutes and seconds.

- wherein

1\ right angle = 90^{\circ}

1^{\circ} = 60{}'

1{}' = 60{}''

 

 Angle made by hour hand and minute hand is approx 100^{^{\circ}} degrees for past seven and two minute total length will be approx 16.6{ because there are 60 gaps and each gap having  \frac{360}{60}=6 measurement

\therefore total angle 16.6 X 6 = 99.6 \simeq 100{}'

\frac{5\pi ^{c} }{g}

[\because the hour hand rotates through an angle of 30^{\circ} in one hour or \left ( \frac{1}{2} \right )^{\circ} in one minute.]

 

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